# Indices and Surds

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## Indices and Surds | AS OCR Maths

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 Created by james_hobson over 5 years ago
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Indices and Surds
1 Indices
1.1 Multiplication Rule
1.1.1 x^a * x^b = x^a+b
1.1.2 e.g. 2^2 * 2^3 = 2^5 = 32
1.2 Division Rule
1.2.1 x^a / x^b = x^a-b
1.2.2 e.g. 2^3 / 2^2 = 2^1 = 2
1.3 Power on Power Rule
1.3.1 (x^a)^b = x^a*b
1.3.2 e.g. (2^3)^2 = 2^3*2 = 2^6 = 64
1.4 Power of Zero
1.4.1 x^0 = 1
1.4.2 e.g. 2^0 = 1
1.5 Negative Powers
1.5.1 x^-a = 1/x^a
1.5.2 e.g. 2^-2 = 1/2^2 = ¼
1.6 Fractional Indices
1.6.1 x^a/b = (b√(x))^a
1.6.2 e.g. 8^2/3 = (cube √(8))^2 = 2^2 = 4
2 Surds
2.1.1 a*√(b) + c*√(b) = (a+c)*√(b)
2.1.2 e.g. 4*√(7) + 3*√(7) = 7*√(7)
2.2 Subtraction
2.2.1 a*√(b) - c*√(b) = (a-c)*√(b)
2.2.2 e.g. 4*√(7) - 2*√(7) = 2*√(7)
2.3 Multiplication Rule
2.3.1 √ab = √a * √b
2.3.2 e.g. √2*4 = √2*√4 = 2√2
2.4 Division Rule
2.4.1 √a/b = √a / √b
2.4.2 e.g. √2/3 = √2 / √3
2.5 Rationalising the Denominator
2.5.1 a / √b * √b / √b = a√b / b
2.5.1.1 e.g. 1 / √2 * √2 / √2 = √2 / 2
2.5.2 a / b+√c * b-√c / b-√c = a(b-√c) / (b+√c)(b-√c)
2.5.2.1 e.g. 1 / 2+√2 * 2-√2 / 2-√2 = 2-√2 / 4-2 = 2-√2 / 2